The weak form method for acoustoelastic simulation with arbitrary prestress

TL;DR

This paper introduces a weak form PDE approach for acoustoelastic simulation under arbitrary prestress, providing higher accuracy than traditional methods, especially at low frequencies, and broadening the applicability beyond simple tensile stress conditions.

Contribution

The paper develops a novel weak form PDE modeling method for acoustoelastic simulation that handles arbitrary prestress states, improving accuracy over existing methods.

Findings

The proposed method closely matches theoretical solutions.

It outperforms the Effective Elastic Constants method at low frequencies.

The approach is validated through numerical simulations of different propagation directions.

Abstract

Acoustoelastic theory has been widely used to evaluate the residual stress (or prestress). However, most of the research remains focused on plate under simple tensile stress condition. In this paper, we propose a new approach: using weak form PDE modeling for acoustoelastic simulation. In the theory part, the weak form of acoustoelastic theory and semi-analytical finite element (SAFE) method is derived. In the numerical simulation part, two cases: the propagation direction is perpendicular to the prestress and parallel to the prestress are presented. The results are compared with the superposition of partial bulk wave (SPBW) method and the previously commonly used Effective Elastic Constants (EEC) method. The results show that the method proposed in this paper is highly accurate. Compared to the EEC method, this approach has no theoretical flaws and aligns more closely with the theoretical solution, especially in the low frequency range where the EEC method's results are almost incorrect. This study provides an accurate method for the simulation of acoustoelasticity.